# Using Rayleigh Quotient to approximate the first eigenvalue of the Laplace operator on the unit disk

Let $D\subset\mathbb{R}^{2}$ unit disk, the first eigenvalue of the Laplace operator holds:

$\lambda_{1}=\inf\left\{ \frac{\int_{D}\left|\triangledown f\right|^{2}dv}{\int_{D}\left|f\right|^{2}dv}\,\,\mid\,\, f\in C_{c}^{\infty}\left(D\right)\right\}$

I know that $5<\lambda_{1}<6$ but I wish to have this result using the Rayleigh quotient

Thank you for your help.

-